The abundance of silent ending consonants in French totally separates its pronunciation from the other Romance languages-- neither Spanish, nor Portuguese, nor Italian, nor Latin have that feature (I'm not sure if they ever did in the past.)

Do etymologists know where, when, and how French acquired its silent and nasalized ending consonants?

About "The abundance of silent ending consonants in French totally separates its pronunciation from the other Romance languages", please notice that this trait is common with a lot of dialects of Catalan and Occitan, so it's not so uncommon among romance languages.
– PereJul 10 '18 at 18:01

@porque_no_les_deux Just compare the litteral prononciation of août and and august in English and Augustus in Latin : the month août is no longer pronnonciated as it is written. Remember French is mostly written as the orthrograph reform of 1835 : things were prononced differently : that’s why for example château isn’t written chateau… Because of the different prononciation on a… Le r des verbes a l’infinitif se prononçait aussi…
– user2284570Jul 12 '18 at 3:41

5 Answers
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This is a huge question. If someone has the time to give a more thorough overview, I invite them to, but here's a quick set of points to consider.

Most of these end consonants are no mystery: they come directly from Latin (temps < tempus, pas < passum, roux < rossus, etc.).

In Latin, there are regular rules for word stress, and they are rarely on the last syllable (exceptions include some inflected forms and single-syllable words).

The end of a syllable (the coda) is among the "weak" phonological positions, where what is called lenition tends to take place. The same generally goes for a word, where the farther something is from the stress, the less loud it tends to be.

Words thus "eroded" over time, from the end gradually back to the stressed syllable, and then to the vowel of the stressed syllable (the loudest part). What we hear in French is often the last, loudest point of the word as it existed in Latin.

Not all consonants disappear at equal rates. Some of the most sonorant, e.g. r and l, usually are still pronounced. Some didn't fully disappear but just became voiceless, like f < v in the suffix -if < -īvus (e.g. sportif). Others like n disappeared but only by leaving a mark in the form of a nasalized vowel where they used to be. There was also an intermediate stage where some instances of l went through a weakened u on their way out and left diphthongs that eventually turned into single, but different vowels: faux < faulx < ... fals < falsus.

In certain contexts, the final consonant is preserved. For example, je prends /pʁɑ̃/ vs. que je prenne /pʁɛn/. This is because the vowel has "taken the bullet" instead; the e has become silent (in many dialects), leaving the n.

Despite those letters falling away, the process was not yet complete by the time the spelling began to be widespread and then standardized and reformed. That is, when the spelling veux was widely adopted, the letters more or less all had a value. But the process of erosion continued, leaving us with these redundant letters.

For "reformed", note jlliagre's comment about certain letters from Latin that were lost but were later restored by classicists. That means some silent letters are deliberate. Blame who you will!

Nevertheless, linguists are interested in exactly what status these letters have. For example, taking petit /pə.ti/ the feminine is petite /pə.tit/. The t ends up being pronounced. For those who can read this is easy to explain, but illiterate speakers also do this! How do they know which consonant to add to petit to form the feminine if they've never seen it written? Worse, it's not always the same consonant: petit(e), chien(ne), vif(/ve), pompier(/ère), etc. So does every word have a separate rule for which consonant to add? Or do the words still have their final consonant in the mental dictionary, and a single uniform rule deletes it in the masculine?

All languages undergo phonological change, and there are certain major trends, but they apply unevenly. Although French and the other Latinate languages are genetically related, they've been separate for so long that they're as different as two species of the same family.

For example, taking the Latin word homō (inflected homin-) "man", French happened to eliminate the unstressed syllable in the middle, leaving mn, and then assimilated those two nasals to mm in homme. The story in Spanish was similar but it ended up dissimilating them by turning the second m into an r in hombre. This shows that we can explain why something happened, but it's hard to predict what will happen next because there are multiple possibilities.

Also note that the letter loss is not unique to French, as Eau qui dort wrote, but in other Latinate languages it's mostly limited to certain dialects or the letters disappeared with the sounds and were never restored.

That should give you the basic idea of what's going on. The comments and other answers all give useful supplementary information.

I'd just throw in that -x has a more unusual backstory: it started as the abbreviation of -us, then people started putting the u's, but without restoring the original -s, and voila! irregular plurals! Other mute letters that were restored include the -t in -nts plural: the plural of, say, arrangement was in fact arrangemens for a while (well, I think it may have been arrangemenz, but let's not split hairs) because the -t wasn't pronounced in that form.
– CirceusJul 9 '18 at 19:51

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z=/ts/ though @Circeus. As for the answer, if you want to add similar final consonant loss in Latin or major Romance languages, there's the loss of final /d/ in Old Latin (dat sg aquād to classical aquā), the loss of final /m/ in Vulgar Latin (with an intermediate nasal vowel stage) and the loss of final /s/ in Andalucian Spanish, triggering vowel quality changes (the same thing happened in French with /as/ > /ɑ/ and with other vowels in Western Oïl varieties)
– Eau qui dortJul 9 '18 at 20:33

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Continuing to include historical consonants that have become silent is very much a thing in English as well. One notable example is the "gh" in words such as "light" - it was originally the guttural sound spelled "ch" in German, which most dialects of English no longer have.
– Robert ColumbiaJul 10 '18 at 12:12

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@MathieuGuindon The spelling adds a vowel, but the actual pronunciation adds a consonant /t/. Because that question is about illiterate people, I'm concerned with pronunciation. :)
– Luke SawczakJul 10 '18 at 14:43

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I'm sure illiterate French are still very familiar with masculine and feminine versions of words. It's not like they've never heard "petite" before and have to guess the pronunciation solely from "petit".
– CJ DennisJul 12 '18 at 4:47

In addition to Luke's answer, here are some comments about each of your examples:

Temps was often written tems, tens or even tans in Old French. When French spelling was standardized, the variant including p, despite being already silent, was selected because it reminds the p that was present in Latin. The ending s was pronounced at that time.

Unlike other Romance languages that have a phonetic orthography, and routinely changed word spelling to adapt to the pronunciation, French is much more conservative and often reluctant to accept such changes.

It is obvious when you observe the strong reactions to the 1990 reform that suggests using the logical ognon (which already failed to survive a previous reform) and nénufar instead of the etymologically bogus nénuphar.

Compare with Spanish which has no problem with nenúfar, elefante or fútbol.

Roux was originally written ros or rous, then, as Circeus wrote, us became x to save parchment leading to rox. After a while, the x trick was forgotten and the u was restored to match the pronounced vowel.

Note also that there are some cases where consonants that were no more pronounced started to be heard again. This happened with infinitive ending -ir (e.g. partir which was pronounced parti). This is occurring now with the p in dompteur. In English, the t in often follows kind of a similar pattern.

Regional variations do also exist for a few words like persil or vingt where the last consonant is pronounced or not depending on the locutor.

One of the reasons the remaining words in your list have their ending consonant preserved is that it is pronounced when the liaison is made:

pas assez (mandatory)

deux ans (mandatory)

beaucoup aimé (optional)

chez eux (mandatory)

petit homme (mandatory)

French would have been even more complex if we had different spellings depending on which word follows another.

Re: "French would have been even more complex should we have different spellings depending of what word follows some words": Well, but we do have that: consider e.g. "Qu'en pense-t-elle ?" and "Vas-y !" (And that's only counting cases where, as in your liaison examples, we're just inserting a consonant. If we count other sorts of changes, then we also have bel homme, cet homme, vieil homme, l'homme . . .)
– ruakhJul 10 '18 at 6:02

@ruakh There are indeed cases where the spelling is affected by the following word.
– jlliagreJul 10 '18 at 9:11

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@MathieuGuindon ruakh's point is beau, vieux, ce change their spelling (and pronunciation) to bel, vieil and cet because of the following world characteristics. Le and la also have their spelling affected.
– jlliagreJul 10 '18 at 22:06

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@MathieuGuindon You are missing the point. Nobody wrote random rules affect some word spelling change (despite liaison presence being sometimes unpredictable). In my reply I actually wrote French words do not change their spelling depending on what word follows, i.e. we write un petit homme where the ending t is pronounced but we do not write un peti garçon because that t is not. Ruakh rightly pointed a few exceptions to this "rule".
– jlliagreJul 10 '18 at 23:53

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@jlliagre For the gerund/infinitive, here it depends on the verb: "I suggest doing X" but "I hope to do X". Either one could also be "I suggest/I hope (that) you do X". For "what/which", there are two cases. When selecting from known options, "which" is standard and "what" is populaire ("Which car should I choose?" ~ "What car should I choose?"). But when identifying a referent, "what" is standard: "I stole a car? I don't know what car you're talking about." (And then "which" would imply a set of possible stolen cars; you concede that you've stolen some but you don't know which one he means.)
– Luke SawczakJul 11 '18 at 16:52

So far and from a standpoint of scientific linguistics, Luke’s answer is the best one. For the sake of completeness and for those interested in the quirky side of things, here is a more formal rendering of the things involved:

Contrary to native speakers of English, native speakers of French acquire two grammars of their language in the course of becoming adults: Modern Oral French (MOF, coming with noticeable regional disparities) and Written Standard French (WSF, which is internationally taught in schools). These two “varieties” of French have different parameter settings for their grammars resulting in divergent typologies. WSF is the older one and its grammar functions mostly according to the rules of Old French. The historical change from Old French to Modern Oral French underlying the typological gap between WSF and MOF amounts to a shift in implementing grammatical features on lexical items from the right edge to the left, a shift a native speaker of French must familiarize himself with earlier (in school) or later and which most speakers never succeed in mastering fully.

WSF is largely suffical in implementing person, number, gender, case and intervening agreement features on lexical items such as verbs and nouns. In a sentence such as [Je [vend-s [le-s poule-s vivant-e-s]]], Je is the grammatical subject, the -s suffixed on vend agrees with the subject in person and number, the -e agreement suffix on vivant indicates that the poule complement is feminine, the -s suffixed on poule indicates its plurality, and the suffix -s on le and vivant-e indicates that they agree in number with poule.

MOF is predominantly prefixal in this respect. In [(Moi) [j-lé-van [lé-poul vivan+t]]], Moi is the grammatical subject which may be null, le j prefixed to lé-van agrees with the underlying subject in person and number, the +t is a so-called “floating” (or latent) consonant which indicates that the poule complement is feminine, the lé- prefixed on poule indicates its plurality, the lé- prefixed to the verb agrees with the *lé- prefixed to the direct object poul in number which is a very Bantu-like feature. Besides the edge reversal, what is also very new is that the masculine form of the adjective is derived from the feminine base by deleting the floating consonant which in reading the adjective aloud in a WSF text becomes “silent”. Suffixes on nouns have altogether disappeared and become a lot fewer on verbs: the 2nd person plural suffix -é, the conditional -rè or -ré (depending on the regional variety), the negative future -ra-pa, and the imperfect -è or -é, the later impeding the deletion of floating consonants in verbs such as in fini+s, imperfect fini+s-è, but fini-ra-pa. More prefixed modalities occur with the progressive antrind-fini-r or aprè-fini-r, the future I va-fini-r, and the future II pour-fini-r as in Moué chu-pour-la-fini-r la-djob, with the bonus of a univerbated chu totally opaque in most varieties if not all basilectal varieties.

Silent consonants in WSF texts are not “acquired”, as one competing answer would have it. As a general rule, before becoming “silent”, they were fully pronounced in Old French and silencing (or muting) amounts to a loss of phonetic realization over time. Learned restorations of Latin consonants in the course of standardization (such as the p in temps) are rather rare and unproblematic. However, silent consonants come in two different kinds, those that are silent for forever such as the plural -s and the p in temps; and those which in MOS float as +C to become silent only when occurring in context which are fully rule-governed.

Interestingly, working artificial intelligence models for spoken French are based on the MOF model of things. Models that need a subcomponent for silent consonants with ad hoc rules for silencing are problematic. As it is, only second language learners have the "chance" to acquire both grammars of French in an order that is not chronologically inverse, going from WSF to MOF.

The Five Faces of Language Change

1. Sound Change: Defining Deviance Downward

Much of the difference between the Latin and the French sentences is due to the fact that in all languages, there is a strong tendency for sounds to erode and disappear over time, especially when the accent does not fall upon them. This is part of what transformed femina "woman" in the Latin sentence into femme in the French one, which is pronounced simply "FAHM." The first syllable of femina was accented -- "FEH-mee-nah"; the other two were not, and over time they weakened and dropped off completely. In real time, we process this kind of erosion as sloppy: to us, Jeet yet? is a barefoot version of Did you eat yet?, as inevitable but formally unsavory as an unmade bed. But this very process was part of what turned Latin into French, and not "sloppy" French but the toniest formal French.

Sounds do not vanish in a heartbeat; at first, there is just a tendency to pronounce the sound less distinctly in casual, running speech. What follows is a kind of analogue of "defining deviance downward," a societal trend in which the gradual acceptance of behaviors once considered taboo has the effect of rendering behaviors of the next level of extremity easier to contemplate and fall into ("If smoking pot is no big deal, then why not...?").

A generation that grows up hearing the sound produced less distinctly most of the time gradually comes to take this lesser rendition of the sound as the "default." Meanwhile, however, they, too, follow the general and eternal tendency to pronounce unaccented sounds less distinctly and thus pronounce their "default" version of the sound, already less distinct than the last generation's, even less distinctly. The next generation takes this muffled sound as "default"; but when they in turn follow the natural tendency to pronounce this sound even less distinctly much of the time, this time there is so little left of the sound that to muffle it is to eliminate it completely. Thus, for them, the choice is between making the sound at all and leaving it off completely. Finally comes a generation for whom the "default" is no sound in that position at all.

This erosion has a particularly dramatic effect in that, whereas some sounds in a word serve no particular purpose (the -ina of fem-ina), other sounds are part of suffixes or prefixes that perform important grammatical functions. For example, think of the -ed that marks past in English; without this suffix, one does not know from the word whether walked is present or past at all. The erosion of prefixes and suffixes like these was particularly central in turning the Latin sentence into the French one. There is a certain tendency for sound change to "go easy on" these prefixes and suffixes to preserve important aspects of the language's machinery. But this is only a tendency, and just as often sound change wreaks its termite-like destruction even on the support beams of a grammar.